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#include<ctime> #include<cstdio> #include<cstring> #include<cstdlib> #include<map> #include<set> #include<queue> #include<deque> #include<stack> #include<bitset> #include<vector> #include<algorithm> #include<iostream> using namespace std;
namespace mine { typedef long long ll; const int INF=0x3f3f3f3f; #define FR first #define SE second #define MP make_pair
const int MAX_NUM=1e4; bool no[MAX_NUM]; int pr=0,prime[MAX_NUM],phi[MAX_NUM]; void () { for(int i=2;i<MAX_NUM;i++) { if(!no[i]) prime[++pr]=i,phi[i]=i-1; for(int j=1;j<=pr and (ll)i*prime[j]<MAX_NUM;j++) { int t=i*prime[j]; no[t]=1; if(i%prime[j]==0) {phi[t]=phi[i]*prime[j];break;} phi[t]=phi[i]*(prime[j]-1); } } }
int MOD=1004535809,M; ll qpower(ll x,ll e,ll MOD) { ll ans=1; while(e) { if(e&1) ans=ans*x%MOD; x=x*x%MOD;e>>=1; } return ans; } ll inv(ll x,ll MOD) {return qpower(x,MOD-2,MOD);} ll add(ll x,ll y) { x+=y; if(x>=MOD) x-=MOD; if(x<=-MOD) x+=MOD; return x; }
bool check(int g,int num) { int tmp=phi[num]; for(int i=1;i<=pr and (ll)prime[i]*prime[i]<=tmp;i++) if(tmp%prime[i]==0) { if(qpower(g,phi[num]/prime[i],num)==1) return 0; while(tmp%prime[i]==0) tmp/=prime[i]; } return qpower(g,tmp,num)!=1; } int getyg(int num) { for(int g=2;g<num;g++) if(check(g,num)) return g; return -1; }
const int MAX_N=MAX_NUM*4; struct Ntt { int R[MAX_N]; void preR(int n) { R[0]=0;for(int i=1;i<n;i++) R[i]=(R[i>>1]>>1)|((i&1)<<((int)log2(n)-1)); } ll w[2][MAX_N]; void prew(int n) { ll g=qpower(3,(MOD-1)/n,MOD),g2=inv(g,MOD); w[0][0]=w[1][0]=1; for(int i=1;i<n;i++) w[0][i]=w[0][i-1]*g%MOD,w[1][i]=w[1][i-1]*g2%MOD; } void solve(ll A[],int n,int f) { for(int i=0;i<n;i++) if(i<R[i]) swap(A[i],A[R[i]]); for(int ln=1;ln<=n/2;ln<<=1) for(int st=0;st<n;st+=ln*2) for(int k=0;k<ln;k++) { ll a=A[st+k],b=w[f][k*(n/(ln*2))]*A[st+ln+k]%MOD; A[st+k]=add(a,b);A[st+ln+k]=add(a,-b); } } }ntt; ll ans[MAX_N],A[MAX_N],C[MAX_N]; void cheng(int ln,int n,ll X[],ll Y[]) { memcpy(C,Y,sizeof C); ntt.solve(X,ln,0);ntt.solve(C,ln,0); for(int i=0;i<ln;i++) X[i]=X[i]*C[i]%MOD; ntt.solve(X,ln,1); for(int i=0;i<n;i++) X[i]=(X[i]+X[n+i])*inv(ln,MOD)%MOD,X[n+i]=0; } void power(int n,int e) { int ln=1;while(ln<4*n) ln<<=1;
ntt.preR(ln);ntt.prew(ln); ans[0]=1; while(e) { if(e&1) cheng(ln,n,ans,A); e>>=1;cheng(ln,n,A,A); } }
bool app[MAX_N]; void main() { pre(); int k,wt,n;scanf("%d%d%d%d",&k,&M,&wt,&n); for(int i=1;i<=n;i++) {int t;scanf("%d",&t);app[t]=1;} int g=getyg(M); bool bk=1; for(int now=1,t=0;t<=M-2;t++,now=now*g%M) { if(app[now]) A[t]=1; if(bk==1 and now==wt) wt=t,bk=0; } power(M-1,k); printf("%lld",(ans[wt]+MOD)%MOD); } }; int main() { srand(time(0)); mine::main(); }
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